Primary coil of a transformer is connected to \(220 \mathrm{~V}\) ac. Primary and secondary turns of the transforms are \(100\) and \(10\) respectively. Secondary coil of transformer is connected to two series resistance shown in shown in figure. The output voltage \(\left(\mathrm{V}_0\right)\) is _______.

Match List\(-I\) with List\(-II\).

List\(-I\)	List\(-II\)
\((A)\) Angular momentum	\((I)\) \(\left[ ML ^2 T ^{-2}\right]\)
\((B)\) Torque	\((II)\) \(\left[ ML ^{-2} T ^{-2}\right]\)
\((C)\) Stress	\((III)\) \(\left[ ML ^2 T ^{-1}\right]\)
\((D)\) Pressure gradient	\((IV)\) \(\left[ ML ^{-1} T ^{-2}\right]\)

Choose the correct answer from the options given below:

A particle executes simple harmonic motion and is located at \(x = a, b\)  and  \(c\) at times \(t_0, 2t_0\) and \(3t_0\) respectively. The frequency of the oscillation is

A transparent cube of side \(d\), made of a material of refractive index \(\mu_2\), is immersed in a liquid of refractive index \(\mu_1(\mu_1 < \mu_2)\). A ray is incident on the face \(AB\) at an angle \(\theta \) (shown in the figure). Total internal reflection takes place at point \(E\) on the face \(BC\). The \(\theta\) must satisfy

In the figure given below. a block of mass \(M =490\,g\) placed on a frictionless table is connected with two springs having same spring constant \(\left( K =2 N m ^{-1}\right)\). If the block is horizontally displaced through ' \(X\) 'm then the number of complete oscillations it will make in \(14 \pi\) seconds will be \(.........\)

The time period of simple harmonic motion of mass \(\mathrm{M}\) in the given figure is \(\pi \sqrt{\frac{\alpha M}{5 K}}\), where the value of \(\alpha\) is _______.

In the given circuit, the equivalent resistance between the terminal \(A\) and \(B\) is \(........\Omega\).

A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of \(10 \mathrm{~N}\) is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is _______ \({N}\).

A point source is emitting sound waves of intensity \(16 \times 10^{-8} \mathrm{Wm}^{-2}\) at the origin. The difference in intensity (magnitude only) at two points located at a distances of \(2 \mathrm{~m}\) and \(4 \mathrm{~m}\) from the origin respectively will be _______ \(\times 10^{-8} \mathrm{Wm}^{-2}\)

The displacement of a damped harmonic oscillator is given by \(x\left( t \right) = {e^{ - 0.1\,t}}\,\cos \left( {10\pi t + \varphi } \right)\)  The time taken for its amplitude of vibration to drop to half of its initial value is close to .... \(s\)

A car moving with a speed of \(54\) km/h takes a turn of radius \(20\) m. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take \(g=10\) m/s\(^2\))

Consider a cylindrical tank of radius \(1 m\) is filled with water. The top surface of water is at \(15\,m\) from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of \(5\,m\) from the bottom. A force of \(5 \times 10^{5} N\) is applied an the top surface of water using a piston. The speed of efflux from the hole will be. (given atmospheric pressure \(P_{A}=1.01 \times 10^{5}\,Pa\), density of water \(\rho_{ w }=1000\,kg / m ^{3}\) and gravitational acceleration \(g=10\,m / s ^{2}\) )

The maximum speed of a boat in still water is \(27 \mathrm{~km} / \mathrm{h}\). Now this boat is moving downstream in a river flowing at \(9 \mathrm{~km} / \mathrm{h}\). A man in the boat throws a ball vertically upwards with speed of \(10 \mathrm{~m} / \mathrm{s}\). Range of the ball as observed by an observer at rest on the river bank, is _______ cm. (Take \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\))